Let the total distance of the trip be d. And let x be the required speed on the second half of the trip.
Time for first half of trip = d/(2 x 36) hours.
Time for second half of trip = d/2x.
The total time for the trip is then:
[tex]\frac{d}{72}+\frac{d}{2x}=\frac{d(x+36)[tex]\frac{d}{45}=\frac{d(x+36)}{72x}[/tex]}{72x}[/tex]
However the total time for the trip must also be d/45.
Therefore we can write and solve the following equation:
[tex]\frac{d}{45}=\frac{d(x+36)}{72x}[/tex]
Dividing both sides by d, and then cross-multiplying gives:
[tex]72x=45x+(36\times45)[/tex]
27x = 1620
x = 60
The answer is 60 mi/h.
